Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints
Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints
复制标题
DOI：
10.1007/s00158-016-1512-4
复制
发表时间：
2016-06
影响因子：
3.9
通讯作者：
F. Feppon;G. Michailidis;M. Sidebottom;G. Allaire;B. Krick;N. Vermaak
中科院分区：
文献类型：
--
作者：
F. Feppon;G. Michailidis;M. Sidebottom;G. Allaire;B. Krick;N. Vermaak
材料的磨损仍然是具有滑动表面的机械系统的寿命和性能的限制因素。随着对低磨损材料需求的增长，对系统优化摩擦学系统的模型和方法的需求也在增长。弹性地基模型为研究多材料复合材料在磨料滑动作用下的磨损提供了一个简化的框架。以前，不断发展的磨损曲线已被证明收敛到一个稳定的状态，其特征在于由一个时间无关的椭圆方程。在本文中，稳态公式进行了推广，并结合形状优化，以改善双材料复合材料的磨损性能。宏观结构和周期性材料的微观结构被认为是。几个常见的摩擦学目标进行磨损系统的识别和数学形式化的形状导数。这些措施包括（i）实现多材料复合材料的平面磨损表面和（ii）最大限度地减少在达到稳态磨损之前的材料损失量。提出了一种基于水平集的拓扑优化算法。特别是，开发了一种新的计划来更新材料界面;该计划（i）方便地在每次迭代时强制执行体积约束，（ii）使用周长惩罚控制设计特征的复杂性，以及（iii）用拓扑梯度使孔或夹杂物成核。广泛的适用性所提出的配方磨损以外的问题进行了讨论，特别是对于方便的控制的几何特征的复杂性是期望的问题。
The wear of materials continues to be a limiting factor in the lifetime and performance of mechanical systems with sliding surfaces. As the demand for low wear materials grows so does the need for models and methods to systematically optimize tribological systems. Elastic foundation models offer a simplified framework to study the wear of multimaterial composites subject to abrasive sliding. Previously, the evolving wear profile has been shown to converge to a steady-state that is characterized by a time-independent elliptic equation. In this article, the steady-state formulation is generalized and integrated with shape optimization to improve the wear performance of bi-material composites. Both macroscopic structures and periodic material microstructures are considered. Several common tribological objectives for systems undergoing wear are identified and mathematically formalized with shape derivatives. These include (i) achieving a planar wear surface from multimaterial composites and (ii) minimizing the run-in volume of material lost before steady-state wear is achieved. A level-set based topology optimization algorithm that incorporates a novel constraint on the level-set function is presented. In particular, a new scheme is developed to update material interfaces; the scheme (i) conveniently enforces volume constraints at each iteration, (ii) controls the complexity of design features using perimeter penalization, and (iii) nucleates holes or inclusions with the topological gradient. The broad applicability of the proposed formulation for problems beyond wear is discussed, especially for problems where convenient control of the complexity of geometric features is desired.